prove that sum of two int-angles = sum of two ext-angles in a quadrilateral

Question

prove that in any quadrilateral the sum of the external angles at two vertices is equal

to the sum of the internal angles at the two vertices.

Answer 1

Quadraliteral have 4 sides.

Sum of interior angles of polygon  = (n-2)180

Here n = 4

= (4-2)180

= 2*180 = 360

Sum of interior angles of quadraliteral = 360

Each exterior angle of a polygon = 360/n

= 360/4 = 90

Quadraliteral have 4 sides, So sum of exterior angle of quadraliteral = 90+90+90+90 = 360

Sum of interior angles of quadraliteral  = sum of exterior angle of quadraliteral = 360 degrees.